In a tensioning device of one type, as disclosed in U.S. Pat. No. 2 337 591, a cam is pivotally mounted on a pin and supports a tension roller adapted to rotate on its outer surface. A flat coil spring extends between a projection extending from the side of the cam and the pin for preloading the tension roller with respect to the pin in the pivotal direction, thus allowing the cam to pivot during operation, to maintain an even tension on the drive belt. Due to the fixed position of the tensioning device, tolerances in the length of the drive belt or similar effects resulting from a non-uniform arrangement of the driving gear parts or variations in diameter of the driving gear, can be compensated only by subsequent adjustment within the effective pivot range of the tensioning device. The range of subsequent adjustment, however, is greatly limited and, for an actual pivot angle of about 60 degrees, it is often less than is needed to compensate for tolerances, in particular during operation. In addition, the tension force of the tensioning device depends on the pivot angle so that the required compensation of tolerances within the pivot rang always results in different tension forces. In order to eliminate this disadvantage, the above arrangement enables the adjustment of the spring end on the side of the pin by means of a slotted disk. Such adjustment cannot be reliably implemented during the mounting process, however, and may lead to unsolvable problems in the crowded space usually available in motor vehicles.